As long as the auxiliary metric \(Z_2=Z_2^\dagger \,\) 
in \({\cal H}_{math}={\cal R}_2\,\) 
is tractable as the (possibly, generalized)
parity [1]}, we will finally define the
intermediate-space Hermitian conjugation
as follows,
\({\cal T}_{[1]}: |\psi \rangle \ \rightarrow \ \langle _{[1]} \psi |\ \equiv \ \langle \psi |\,Z_2\,.\) 
